Summary: TRIANGLES OF BAUMSLAG-SOLITAR GROUPS
Abstract. Our main result is that many triangles of Baumslag-
Solitar groups collapse to finite groups, generalizing a famous ex-
ample of Hirsch and other examples due to several authors. A
triangle of Baumslag-Solitar groups means a group with three gen-
erators, cyclically ordered, with each generator conjugating some
power of the previous one to another power. There are six param-
eters, occurring in pairs, and we show that the triangle fails to be
developable whenever one of the parameters divides its partner, ex-
cept for a few special cases. Furthermore, under fairly general con-
ditions, the group turns out to be finite and solvable of class 3.
We obtain a lot of information about finite quotients, even when
we cannot determine developability.
We study groups G of the form
(1) G(a, b; c, d; e, f) := x, y, z (xa